Game Goal:
Given a pattern of blue and pink gates, find a minimum sequence of ladybug
runs that turns all the gates pink. (Click on any 'start' to start the
ladybug)

Current
Controls

1. Click
on any of the three 'start' entry points in the first row of tiles, to
start the ladybug down that path. Note that: (a) the
ladybug always chooses the path for which the gate immediately below is
open, i.e. either 'west open' (blue) or 'east open' (pink),(b) each
gate changes to the opposite state as the ladybug passes through it,(c) the
path that they ladybug is currently traversing is traced in white, so that
the player can review the current run before starting the ladybug again.

2. You can
reset all the gates to blue by clicking on the 'reset' tile in the far
left hand column.

3. You can
create your own pattern by first clicking on the 'Create pattern' tile
in the far left hand column, and then clicking on any gate to toggle its
color. Note that some patterns aren't reachable (i.e. in the orbit of the
initial all blue state), and so, for each pattern you create, whether or
not it is valid is displayed in the far left hand column.

4. You can
speed up or slow down the ladybug by clicking on the 'faster ladybug' ('slower
ladybug') tile in the far left hand column.

5. In order
to see the effect of running the ladybug through each entry point a selected
number of times, without actually running the ladybug, you can click on
the 'autorun' tile in the far right hand column. Next, choose how many
times you want the ladybug to go through each entry point, and then click
on the 'start autorun' tile in the far right hand column.

In addition
to being an entertaining diversion, this second variation can be used as
a supplement to Richard Singer's paper, Think-A-Dot
Group, which is a fascinating exploration of group theoretic concepts
emerging from a similar device, leading ultimately to a very well motivated
proof of the fundamental theorem of finite abelian groups.